Such a hook is shown in Dutch Patent Application 9201957 (not a prior publication) in the name of Eisenkolb Confectiemachines B.V. This patent application also describes a device by means of which a curtain hook can be moved automatically to a needle plate below a sewing machine, following which a stop element is operated to prevent the hook from sliding back. In this position of the curtain hook a curtain pleat can be brought in such a way that the strip and the I-section of the curtain hook fall into the pleat. A sewing machine clamp (pressure foot) is then operated in order to fix material and curtain hook, and the curtain hook can be sewn into the curtain pleat, the needle passing through the strip right next to the I-section. Said sewing machine clamp also presses on the runner. It has been found that this causes the hook to go into a slanting position, with the result that the stitching becomes curved and does not run in a straight line at right angles to the curtain edge. Besides, there is relatively little space present between the bottom side of the curtain hook and the needle plate of the sewing machine and between the top side of the curtain hook and the pressure foot of the sewing machine, which can give rise to problems when the curtain pleat is being slid over the curtain hook, in particular if the curtain is made of relatively thick, coarse material.